)) Use algebra tiles to find $$ \left(7 x^{2}+5 x-6\right)-(-10 x-3) $$

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UpStudy AI · Accepted Answer

To solve the expression $$ \left(7x^{2} + 5x - 6\right) - \left(-10x - 3\right) $$ using algebra tiles, let's break it down step by step.

### Step 1: Understand the Components

1. **First Polynomial:** $$ 7x^{2} + 5x - 6 $$
   - **$$7x^{2}$$**: Represents seven $$x^2$$ tiles.
   - **$$5x$$**: Represents five $$x$$ tiles.
   - **$$-6$$**: Represents six negative unit tiles.

2. **Second Polynomial (to be subtracted):** $$ -10x - 3 $$
   - **$$-10x$$**: Represents ten negative $$x$$ tiles.
   - **$$-3$$**: Represents three negative unit tiles.

### Step 2: Subtract the Second Polynomial

Subtracting $$ (-10x - 3) $$ is equivalent to adding its opposite:

$$
\left(7x^{2} + 5x - 6\right) + \left(10x + 3\right)
$$

### Step 3: Combine Like Terms Using Algebra Tiles

1. **Combine $$x^2$$ Terms:**
   - $$7x^{2}$$ remains as there are no other $$x^2$$ terms to combine.

2. **Combine $$x$$ Terms:**
   - $$5x + 10x = 15x$$

3. **Combine Constant Terms:**
   - $$-6 + 3 = -3$$

### Step 4: Write the Final Expression

Combine all the simplified terms:

$$
7x^{2} + 15x - 3
$$

### Visual Representation with Algebra Tiles

While I can't provide a visual diagram here, here's how you can imagine the tiles:

- **Positive Tiles:**
  - 7 $$x^2$$ tiles
  - 15 $$x$$ tiles

- **Negative Tiles:**
  - 3 negative unit tiles

Arrange the tiles accordingly to represent the final simplified expression.

### Final Answer

$$
7x^{2} + 15x - 3
$$
$$7x^{2} + 15x - 3$$

)) Use algebra tiles to find \( \left(7 x^{2}+5 x-6\right)-(-10 x-3) \)

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